How is this blendfile hiding textures?
The reason for this is that none were created, the author simply unwrapped the models and changed the view to Textured.

Here is a quick example using the texture I unpacked from the file. As you can see, the cube doesn't even have a material. This is perfectly legit in Blender but really bad practice as it pertains to asset management etc.



Since the objects are already unwrapped, to fix it, just create a texture and change Coordinates under Mapping to UV. For a bit more information on correct UV mapping, see Blender UV mapping error